A product has annual demand of $100,000$ units. The plant manager wants production to follow a four$-$hour cycle. Based on the follolwing data, what setup time will enable the desired production cycle?

d $=400$ per day $(250$ production days per year$)$

p $=4000$ units per day

H $=$ $$40$ per unit per year

Q $=200($demand for four hours, half a day$)$

hourly labor rate $=$ $$18$

$7\mathrm{.}2$ minutes

$16\mathrm{.}0$ minutes

$40\mathrm{.}0$ minutes

$0\mathrm{.}40$ minutes

$24\mathrm{.}0$ minutes